Anna Baccaglini-Frank

Using Digital Environments to Address Students’ Mathematical Learning Difficulties

The need to deal with different cognitive necessities of students in the mathematical classroom, and in particular of students who persistently fail in mathematics, frequently referred to as “having mathematical learning difficulties or disabilities” (MLD), has become an important topic of research in mathematics education and in cognitive psychology. Though frameworks for analyzing students’ difficulties and/or for designing inclusive activities are still quite fragmentary, the literature rather consistently suggests that technology can support the learning of students with different learning characteristics. The focus of this chapter is on providing insight into this issue by proposing analyses of specific software with a double perspective. We will analyze design features of the selected software, based on the potential support these can provide to students’ learning processes, in particular those of students classified as having MLD. We will also analyze some interactions that actually occurred between students and the software, highlighting important qualitative results from recent studies in which we have been involved.

Detecting strengths and weaknesses in learning mathematics through a model classifying mathematical skills

Abstract Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery of mathematical tasks designed to elicit abilities from each domain, that was administered to a sample of 165 typical population 5th and 6th grade students (MLD = 9 and LA = 17). Explanatory and confirmatory factor analysis were conducted on the data obtained, together with K-means cluster analysis. Results indicated strong evidence for supporting the solidity of the model, and clustered the population into six distinguishable performance groups with the MLD and LA students distributed within five of the clusters. These findings support the hypothesis that difficulties in learning mathematics can have multiple origins and provide a means for sketching students’ mathematical learning profiles.

Research in Early Childhood Mathematics Education Today

This edited book brings together a collection of research-based work from different contexts across the globe to contribute to improving knowledge and understanding of major issues that early childhood mathematics education encounters today and to advancing research, development and practice in this field. The chapters of the book are based on the invited contributions in TSG 1: Early Childhood Mathematics Education at ICME-13. The chapters provide a wide scope for discussion of current themes, theoretical perspectives and methodological approaches to promoting teaching and learning of mathematics in the early years. This chapter includes an overview of the core focus of the chapters.

Special Needs in Research and Instruction in Whole Number Arithmetic

This chapter provides an overview of the ICME 23 Study panel on special needs in research and instruction in whole number arithmetic. It starts with a general introduction by Verschaffel about the state of affairs in and the major issues and challenges for research and educational practice in the field of mathematical learning difficulties (MLD). Afterwards these issues and challenges are explored and discussed from four different angles by four scholars with complementary specializations in the domain of children with MLD and/or other special needs in the curricular domain of whole number arithmetic, namely, Anna Baccaglini-Frank, Joanne Mulligan, Marja van den Heuvel-Panhuizen and Yan Ping Xin. Finally, Brian Butterworth discusses these four contributions, particularly with respect to the questions ‘what constitutes the “mathematics” that MLD research and practice should address’ and ‘what can be considered as appropriate interventions for children with special needs’

Whole Number Thinking, Learning and Development: Neuro-cognitive, Cognitive and Developmental Approaches

This chapter focuses on the neuro-cognitive, cognitive and developmental analyses of whole number arithmetic (WNA) learning. It comprises five sections. The first section provides an overview of the working group discussion. Section 7.2 reviews neuro-cognitive perspectives of learning WNA but looks beyond these to explain the transcoding of numerals to number words. In the third section, children’s early mathematics-related competencies in reasoning about quantitative relations, patterns and structures are explored from new theoretical perspectives. Studies presented and discussed in working group 2 are presented in the following section as exemplars of intervention studies. The final section examines methodologies utilized in neuro-cognitive, cognitive and developmental analyses of children’s whole number learning. It discusses study designs and their potentialities and limitations for understanding how children develop competencies with whole numbers as well as task designs in cognitive neuroscience research pertinent to number learning. The chapter concludes with implications for further research and teaching practice.

Early childhood mathematics education: reflections and moving forward

This book brings together creative and insightful current research studies on teaching and learning mathematics in early childhood by scholars from different parts of the world. In this chapter we reflect on this work and discuss the major insights, conclusions, implications and future research directions for early childhood mathematics education. We focus on each of the five key themes of the book: pattern and structure, number sense, embodied action and context, technology and early childhood educators’ professional issues and education.

What Schemes Do Preschoolers Develop When Using Multi-touch Applications to Foster Number Sense (and Why)?

As part of an educational project proposed in Italian pre-schools, an educator followed a protocol that had been used in a previous study (Baccaglini-Frank and Maracci in Digit Exp Math Educ 1:7–27, 2015) proposing two chosen iPad apps to children of ages five to six. This study investigates the schemes developed by the children in response to the apps, and the role the educator’s interventions seemed to play in such development. Analyses of the data collected suggest that her interventions privileged and encouraged schemes involving counting, which limited the variety of schemes enacted and the aspects of number sense strengthened through the protocol.